Consider an American put option with a strike of $21, a spot price of $19, volatility of 25% p.a, risk free rate of 2% p.a continuously compounded, and time to maturity of 6 months. A dividend equal to 3.5% of the then-current stock value is expected in 2 months. Use a three-period binomial model to price the option (assuming the ex-div drop-off occurs at t=2 months). Show all workings